Question

a statistician at a metal manufacturing plant is sampling the thickness of metal plates. if an outlier occurs within a particular sample, the statistician must check the configuration of the machine. the distribution of metal thickness has mean 23.5 millimeters (mm) and standard deviation 1.4 mm. based on the two - standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine?
a 19.3 mm
b 20.6 mm
c 22.1 mm
d 23.5 mm
e 24.9 mm

Explanation:

Step1: Recall outlier rule

Outliers are values more than 2 standard - deviations away from the mean. We want the upper - bound outlier for the greatest thickness.

Step2: Calculate upper - bound outlier

The formula for the upper - bound outlier is $\mu+2\sigma$, where $\mu = 23.5$ mm (mean) and $\sigma = 1.4$ mm (standard deviation). So, $23.5+2\times1.4=23.5 + 2.8=26.3$ mm. We need to find the value among the options that is closest to but less than 26.3 mm.

Step3: Compare options

Among the options A. 19.3 mm, B. 20.6 mm, C. 22.1 mm, D. 23.5 mm, E. 24.9 mm, the greatest value is 24.9 mm.

Answer:

E. 24.9 mm